Properties

Label 392.3.k.j.275.1
Level 392
Weight 3
Character 392.275
Analytic conductor 10.681
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.796594176.2
Defining polynomial: \(x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 83 x^{4} - 104 x^{3} + 22 x^{2} + 24 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.1
Root \(-0.207107 + 2.54762i\) of defining polynomial
Character \(\chi\) \(=\) 392.275
Dual form 392.3.k.j.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.97374 - 0.323042i) q^{2} +(1.70711 + 2.95680i) q^{3} +(3.79129 + 1.27520i) q^{4} +(-1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +O(q^{10})\) \(q+(-1.97374 - 0.323042i) q^{2} +(1.70711 + 2.95680i) q^{3} +(3.79129 + 1.27520i) q^{4} +(-1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +(2.39883 + 1.96308i) q^{10} +(2.24264 + 3.88437i) q^{11} +(2.70163 + 13.3870i) q^{12} -1.54985i q^{13} -5.29150i q^{15} +(12.7477 + 9.66930i) q^{16} +(11.8284 + 20.4874i) q^{17} +(3.36526 - 4.11224i) q^{18} +(-12.4350 + 21.5381i) q^{19} +(-4.10051 - 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +(30.5055 + 17.6124i) q^{23} +(-1.00775 - 27.2951i) q^{24} +(-11.2990 - 19.5704i) q^{25} +(-0.500665 + 3.05899i) q^{26} +21.6569 q^{27} +22.4499i q^{29} +(-1.70938 + 10.4440i) q^{30} +(-40.4569 + 23.3578i) q^{31} +(-22.0371 - 23.2027i) q^{32} +(-7.65685 + 13.2621i) q^{33} +(-16.7279 - 44.2579i) q^{34} +(-7.97056 + 7.02938i) q^{36} +(-50.7340 - 29.2913i) q^{37} +(31.5012 - 38.4935i) q^{38} +(4.58258 - 2.64575i) q^{39} +(6.59133 + 10.5016i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(3.54915 + 17.5866i) q^{44} +(3.56604 - 2.05886i) q^{45} +(-54.5204 - 44.6168i) q^{46} +(31.2918 + 18.0663i) q^{47} +(-6.82843 + 54.1990i) q^{48} +(15.9792 + 42.2769i) q^{50} +(-40.3848 + 69.9485i) q^{51} +(1.97636 - 5.87591i) q^{52} +(-84.7102 + 48.9075i) q^{53} +(-42.7450 - 6.99607i) q^{54} -6.95149i q^{55} -84.9117 q^{57} +(7.25227 - 44.3103i) q^{58} +(30.7782 + 53.3094i) q^{59} +(6.74773 - 20.0616i) q^{60} +(32.6340 + 18.8412i) q^{61} +(87.3970 - 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} +(-1.20101 + 2.08021i) q^{65} +(19.3968 - 23.7024i) q^{66} +(16.6863 + 28.9015i) q^{67} +(18.7194 + 92.7574i) q^{68} +120.265i q^{69} -102.199i q^{71} +(18.0026 - 11.2993i) q^{72} +(34.6569 + 60.0274i) q^{73} +(90.6733 + 74.2026i) q^{74} +(38.5772 - 66.8176i) q^{75} +(-74.6102 + 65.8000i) q^{76} +(-9.89949 + 3.74166i) q^{78} +(33.5156 + 19.3503i) q^{79} +(-9.61710 - 22.8567i) q^{80} +(48.9264 + 84.7430i) q^{81} +(-53.2328 - 8.71262i) q^{82} -3.61522 q^{83} -36.6645i q^{85} +(33.8922 + 5.54714i) q^{86} +(-66.3799 + 38.3245i) q^{87} +(-1.32389 - 35.8578i) q^{88} +(22.0294 - 38.1561i) q^{89} +(-7.70354 + 2.91166i) q^{90} +(93.1960 + 105.674i) q^{92} +(-138.129 - 79.7486i) q^{93} +(-55.9256 - 45.7668i) q^{94} +(33.3807 - 19.2724i) q^{95} +(30.9861 - 104.769i) q^{96} -96.1076 q^{97} -11.9167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} + O(q^{10}) \) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} - 28q^{10} - 16q^{11} - 24q^{12} - 8q^{16} + 72q^{17} - 16q^{18} + 8q^{19} - 112q^{20} - 48q^{22} - 40q^{24} + 68q^{25} + 28q^{26} + 128q^{27} - 16q^{33} - 32q^{34} + 72q^{36} - 76q^{38} + 56q^{40} + 80q^{41} - 160q^{43} + 48q^{44} - 224q^{46} - 32q^{48} + 224q^{50} - 176q^{51} - 56q^{52} - 16q^{54} - 272q^{57} + 168q^{58} + 184q^{59} - 56q^{60} + 224q^{62} + 288q^{64} - 168q^{65} - 32q^{66} + 224q^{67} - 216q^{68} + 160q^{72} + 232q^{73} + 280q^{74} + 88q^{75} + 48q^{76} - 336q^{80} + 52q^{81} - 48q^{82} - 176q^{83} - 8q^{86} - 240q^{88} + 312q^{89} - 616q^{90} + 112q^{92} - 112q^{94} + 176q^{96} + 272q^{97} - 480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97374 0.323042i −0.986869 0.161521i
\(3\) 1.70711 + 2.95680i 0.569036 + 0.985599i 0.996662 + 0.0816428i \(0.0260167\pi\)
−0.427626 + 0.903956i \(0.640650\pi\)
\(4\) 3.79129 + 1.27520i 0.947822 + 0.318800i
\(5\) −1.34221 0.774923i −0.268441 0.154985i 0.359738 0.933053i \(-0.382866\pi\)
−0.628179 + 0.778069i \(0.716199\pi\)
\(6\) −2.41421 6.38741i −0.402369 1.06457i
\(7\) 0 0
\(8\) −7.07107 3.74166i −0.883883 0.467707i
\(9\) −1.32843 + 2.30090i −0.147603 + 0.255656i
\(10\) 2.39883 + 1.96308i 0.239883 + 0.196308i
\(11\) 2.24264 + 3.88437i 0.203876 + 0.353124i 0.949774 0.312936i \(-0.101313\pi\)
−0.745898 + 0.666060i \(0.767979\pi\)
\(12\) 2.70163 + 13.3870i 0.225135 + 1.11558i
\(13\) 1.54985i 0.119219i −0.998222 0.0596094i \(-0.981014\pi\)
0.998222 0.0596094i \(-0.0189855\pi\)
\(14\) 0 0
\(15\) 5.29150i 0.352767i
\(16\) 12.7477 + 9.66930i 0.796733 + 0.604332i
\(17\) 11.8284 + 20.4874i 0.695790 + 1.20514i 0.969914 + 0.243449i \(0.0782788\pi\)
−0.274124 + 0.961694i \(0.588388\pi\)
\(18\) 3.36526 4.11224i 0.186959 0.228458i
\(19\) −12.4350 + 21.5381i −0.654475 + 1.13358i 0.327550 + 0.944834i \(0.393777\pi\)
−0.982025 + 0.188750i \(0.939556\pi\)
\(20\) −4.10051 4.64954i −0.205025 0.232477i
\(21\) 0 0
\(22\) −3.17157 8.39119i −0.144162 0.381418i
\(23\) 30.5055 + 17.6124i 1.32633 + 0.765756i 0.984730 0.174090i \(-0.0556985\pi\)
0.341598 + 0.939846i \(0.389032\pi\)
\(24\) −1.00775 27.2951i −0.0419896 1.13730i
\(25\) −11.2990 19.5704i −0.451960 0.782817i
\(26\) −0.500665 + 3.05899i −0.0192563 + 0.117653i
\(27\) 21.6569 0.802106
\(28\) 0 0
\(29\) 22.4499i 0.774136i 0.922051 + 0.387068i \(0.126512\pi\)
−0.922051 + 0.387068i \(0.873488\pi\)
\(30\) −1.70938 + 10.4440i −0.0569792 + 0.348135i
\(31\) −40.4569 + 23.3578i −1.30506 + 0.753478i −0.981268 0.192649i \(-0.938292\pi\)
−0.323795 + 0.946127i \(0.604959\pi\)
\(32\) −22.0371 23.2027i −0.688659 0.725085i
\(33\) −7.65685 + 13.2621i −0.232026 + 0.401881i
\(34\) −16.7279 44.2579i −0.491998 1.30170i
\(35\) 0 0
\(36\) −7.97056 + 7.02938i −0.221405 + 0.195260i
\(37\) −50.7340 29.2913i −1.37119 0.791657i −0.380111 0.924941i \(-0.624114\pi\)
−0.991078 + 0.133284i \(0.957448\pi\)
\(38\) 31.5012 38.4935i 0.828979 1.01299i
\(39\) 4.58258 2.64575i 0.117502 0.0678398i
\(40\) 6.59133 + 10.5016i 0.164783 + 0.262540i
\(41\) 26.9706 0.657819 0.328909 0.944362i \(-0.393319\pi\)
0.328909 + 0.944362i \(0.393319\pi\)
\(42\) 0 0
\(43\) −17.1716 −0.399339 −0.199669 0.979863i \(-0.563987\pi\)
−0.199669 + 0.979863i \(0.563987\pi\)
\(44\) 3.54915 + 17.5866i 0.0806625 + 0.399695i
\(45\) 3.56604 2.05886i 0.0792454 0.0457524i
\(46\) −54.5204 44.6168i −1.18523 0.969930i
\(47\) 31.2918 + 18.0663i 0.665783 + 0.384390i 0.794477 0.607295i \(-0.207745\pi\)
−0.128694 + 0.991684i \(0.541079\pi\)
\(48\) −6.82843 + 54.1990i −0.142259 + 1.12915i
\(49\) 0 0
\(50\) 15.9792 + 42.2769i 0.319584 + 0.845539i
\(51\) −40.3848 + 69.9485i −0.791858 + 1.37154i
\(52\) 1.97636 5.87591i 0.0380070 0.112998i
\(53\) −84.7102 + 48.9075i −1.59831 + 0.922782i −0.606492 + 0.795090i \(0.707424\pi\)
−0.991814 + 0.127693i \(0.959243\pi\)
\(54\) −42.7450 6.99607i −0.791573 0.129557i
\(55\) 6.95149i 0.126391i
\(56\) 0 0
\(57\) −84.9117 −1.48968
\(58\) 7.25227 44.3103i 0.125039 0.763971i
\(59\) 30.7782 + 53.3094i 0.521664 + 0.903549i 0.999682 + 0.0251987i \(0.00802186\pi\)
−0.478018 + 0.878350i \(0.658645\pi\)
\(60\) 6.74773 20.0616i 0.112462 0.334360i
\(61\) 32.6340 + 18.8412i 0.534983 + 0.308873i 0.743043 0.669243i \(-0.233382\pi\)
−0.208060 + 0.978116i \(0.566715\pi\)
\(62\) 87.3970 33.0329i 1.40963 0.532790i
\(63\) 0 0
\(64\) 36.0000 + 52.9150i 0.562500 + 0.826797i
\(65\) −1.20101 + 2.08021i −0.0184771 + 0.0320032i
\(66\) 19.3968 23.7024i 0.293891 0.359127i
\(67\) 16.6863 + 28.9015i 0.249049 + 0.431366i 0.963262 0.268563i \(-0.0865486\pi\)
−0.714213 + 0.699928i \(0.753215\pi\)
\(68\) 18.7194 + 92.7574i 0.275285 + 1.36408i
\(69\) 120.265i 1.74297i
\(70\) 0 0
\(71\) 102.199i 1.43942i −0.694277 0.719708i \(-0.744276\pi\)
0.694277 0.719708i \(-0.255724\pi\)
\(72\) 18.0026 11.2993i 0.250036 0.156935i
\(73\) 34.6569 + 60.0274i 0.474751 + 0.822294i 0.999582 0.0289132i \(-0.00920463\pi\)
−0.524830 + 0.851207i \(0.675871\pi\)
\(74\) 90.6733 + 74.2026i 1.22532 + 1.00274i
\(75\) 38.5772 66.8176i 0.514362 0.890901i
\(76\) −74.6102 + 65.8000i −0.981713 + 0.865789i
\(77\) 0 0
\(78\) −9.89949 + 3.74166i −0.126917 + 0.0479700i
\(79\) 33.5156 + 19.3503i 0.424248 + 0.244940i 0.696893 0.717175i \(-0.254565\pi\)
−0.272645 + 0.962115i \(0.587898\pi\)
\(80\) −9.61710 22.8567i −0.120214 0.285709i
\(81\) 48.9264 + 84.7430i 0.604030 + 1.04621i
\(82\) −53.2328 8.71262i −0.649181 0.106251i
\(83\) −3.61522 −0.0435569 −0.0217785 0.999763i \(-0.506933\pi\)
−0.0217785 + 0.999763i \(0.506933\pi\)
\(84\) 0 0
\(85\) 36.6645i 0.431347i
\(86\) 33.8922 + 5.54714i 0.394095 + 0.0645016i
\(87\) −66.3799 + 38.3245i −0.762987 + 0.440511i
\(88\) −1.32389 35.8578i −0.0150442 0.407475i
\(89\) 22.0294 38.1561i 0.247522 0.428720i −0.715316 0.698801i \(-0.753717\pi\)
0.962838 + 0.270081i \(0.0870505\pi\)
\(90\) −7.70354 + 2.91166i −0.0855948 + 0.0323518i
\(91\) 0 0
\(92\) 93.1960 + 105.674i 1.01300 + 1.14863i
\(93\) −138.129 79.7486i −1.48525 0.857512i
\(94\) −55.9256 45.7668i −0.594953 0.486880i
\(95\) 33.3807 19.2724i 0.351376 0.202867i
\(96\) 30.9861 104.769i 0.322772 1.09134i
\(97\) −96.1076 −0.990800 −0.495400 0.868665i \(-0.664979\pi\)
−0.495400 + 0.868665i \(0.664979\pi\)
\(98\) 0 0
\(99\) −11.9167 −0.120371
\(100\) −17.8815 88.6056i −0.178815 0.886056i
\(101\) 16.9881 9.80808i 0.168199 0.0971097i −0.413537 0.910487i \(-0.635707\pi\)
0.581736 + 0.813377i \(0.302374\pi\)
\(102\) 102.305 125.014i 1.00299 1.22563i
\(103\) −37.3120 21.5421i −0.362252 0.209146i 0.307816 0.951446i \(-0.400402\pi\)
−0.670068 + 0.742300i \(0.733735\pi\)
\(104\) −5.79899 + 10.9591i −0.0557595 + 0.105376i
\(105\) 0 0
\(106\) 182.995 69.1656i 1.72637 0.652506i
\(107\) −7.79899 + 13.5082i −0.0728878 + 0.126245i −0.900166 0.435547i \(-0.856555\pi\)
0.827278 + 0.561793i \(0.189888\pi\)
\(108\) 82.1074 + 27.6168i 0.760253 + 0.255711i
\(109\) −3.33576 + 1.92590i −0.0306033 + 0.0176688i −0.515224 0.857056i \(-0.672291\pi\)
0.484620 + 0.874725i \(0.338958\pi\)
\(110\) −2.24562 + 13.7204i −0.0204148 + 0.124731i
\(111\) 200.013i 1.80192i
\(112\) 0 0
\(113\) −13.7746 −0.121899 −0.0609496 0.998141i \(-0.519413\pi\)
−0.0609496 + 0.998141i \(0.519413\pi\)
\(114\) 167.593 + 27.4300i 1.47012 + 0.240614i
\(115\) −27.2965 47.2789i −0.237361 0.411121i
\(116\) −28.6282 + 85.1142i −0.246795 + 0.733743i
\(117\) 3.56604 + 2.05886i 0.0304790 + 0.0175971i
\(118\) −43.5269 115.161i −0.368872 0.975944i
\(119\) 0 0
\(120\) −19.7990 + 37.4166i −0.164992 + 0.311805i
\(121\) 50.4411 87.3666i 0.416869 0.722038i
\(122\) −58.3245 47.7298i −0.478069 0.391228i
\(123\) 46.0416 + 79.7464i 0.374322 + 0.648345i
\(124\) −183.170 + 36.9655i −1.47718 + 0.298109i
\(125\) 73.7695i 0.590156i
\(126\) 0 0
\(127\) 125.025i 0.984445i −0.870469 0.492223i \(-0.836185\pi\)
0.870469 0.492223i \(-0.163815\pi\)
\(128\) −53.9608 116.070i −0.421569 0.906796i
\(129\) −29.3137 50.7728i −0.227238 0.393588i
\(130\) 3.04248 3.71782i 0.0234037 0.0285986i
\(131\) 50.1751 86.9059i 0.383016 0.663404i −0.608475 0.793573i \(-0.708219\pi\)
0.991492 + 0.130169i \(0.0415519\pi\)
\(132\) −45.9411 + 40.5163i −0.348039 + 0.306941i
\(133\) 0 0
\(134\) −23.5980 62.4344i −0.176104 0.465928i
\(135\) −29.0679 16.7824i −0.215318 0.124314i
\(136\) −6.98264 189.126i −0.0513430 1.39063i
\(137\) −28.6569 49.6351i −0.209174 0.362300i 0.742280 0.670089i \(-0.233744\pi\)
−0.951455 + 0.307789i \(0.900411\pi\)
\(138\) 38.8506 237.371i 0.281526 1.72008i
\(139\) 183.664 1.32132 0.660662 0.750684i \(-0.270276\pi\)
0.660662 + 0.750684i \(0.270276\pi\)
\(140\) 0 0
\(141\) 123.365i 0.874926i
\(142\) −33.0144 + 201.713i −0.232496 + 1.42052i
\(143\) 6.02017 3.47575i 0.0420991 0.0243059i
\(144\) −39.1826 + 16.4863i −0.272101 + 0.114488i
\(145\) 17.3970 30.1324i 0.119979 0.207810i
\(146\) −49.0122 129.674i −0.335700 0.888179i
\(147\) 0 0
\(148\) −154.995 175.748i −1.04726 1.18748i
\(149\) 166.545 + 96.1549i 1.11775 + 0.645335i 0.940826 0.338889i \(-0.110051\pi\)
0.176927 + 0.984224i \(0.443384\pi\)
\(150\) −97.7261 + 119.418i −0.651508 + 0.796123i
\(151\) 99.3791 57.3765i 0.658140 0.379977i −0.133428 0.991058i \(-0.542599\pi\)
0.791568 + 0.611081i \(0.209265\pi\)
\(152\) 168.517 105.770i 1.10867 0.695854i
\(153\) −62.8528 −0.410803
\(154\) 0 0
\(155\) 72.4020 0.467110
\(156\) 20.7477 4.18710i 0.132998 0.0268404i
\(157\) −183.724 + 106.073i −1.17022 + 0.675625i −0.953731 0.300661i \(-0.902793\pi\)
−0.216486 + 0.976286i \(0.569460\pi\)
\(158\) −59.9001 49.0193i −0.379115 0.310249i
\(159\) −289.219 166.981i −1.81899 1.05019i
\(160\) 11.5980 + 48.2199i 0.0724874 + 0.301374i
\(161\) 0 0
\(162\) −69.1924 183.066i −0.427114 1.13004i
\(163\) 120.267 208.309i 0.737835 1.27797i −0.215634 0.976474i \(-0.569182\pi\)
0.953469 0.301493i \(-0.0974849\pi\)
\(164\) 102.253 + 34.3929i 0.623495 + 0.209713i
\(165\) 20.5541 11.8669i 0.124571 0.0719208i
\(166\) 7.13551 + 1.16787i 0.0429850 + 0.00703535i
\(167\) 212.101i 1.27006i −0.772486 0.635032i \(-0.780987\pi\)
0.772486 0.635032i \(-0.219013\pi\)
\(168\) 0 0
\(169\) 166.598 0.985787
\(170\) −11.8442 + 72.3661i −0.0696715 + 0.425683i
\(171\) −33.0381 57.2236i −0.193205 0.334641i
\(172\) −65.1024 21.8972i −0.378502 0.127309i
\(173\) 157.801 + 91.1065i 0.912145 + 0.526627i 0.881121 0.472891i \(-0.156790\pi\)
0.0310245 + 0.999519i \(0.490123\pi\)
\(174\) 143.397 54.1990i 0.824121 0.311488i
\(175\) 0 0
\(176\) −8.97056 + 71.2016i −0.0509691 + 0.404555i
\(177\) −105.083 + 182.010i −0.593691 + 1.02830i
\(178\) −55.8064 + 68.1937i −0.313519 + 0.383111i
\(179\) −28.6030 49.5419i −0.159793 0.276770i 0.775001 0.631960i \(-0.217749\pi\)
−0.934794 + 0.355190i \(0.884416\pi\)
\(180\) 16.1454 3.25830i 0.0896964 0.0181016i
\(181\) 326.212i 1.80228i 0.433533 + 0.901138i \(0.357267\pi\)
−0.433533 + 0.901138i \(0.642733\pi\)
\(182\) 0 0
\(183\) 128.656i 0.703039i
\(184\) −149.807 238.680i −0.814170 1.29717i
\(185\) 45.3970 + 78.6299i 0.245389 + 0.425026i
\(186\) 246.868 + 202.024i 1.32725 + 1.08615i
\(187\) −53.0538 + 91.8919i −0.283710 + 0.491401i
\(188\) 95.5980 + 108.398i 0.508500 + 0.576585i
\(189\) 0 0
\(190\) −72.1106 + 27.2552i −0.379530 + 0.143449i
\(191\) 84.0589 + 48.5314i 0.440099 + 0.254091i 0.703639 0.710557i \(-0.251557\pi\)
−0.263541 + 0.964648i \(0.584890\pi\)
\(192\) −95.0031 + 196.776i −0.494808 + 1.02488i
\(193\) −78.6518 136.229i −0.407522 0.705849i 0.587089 0.809522i \(-0.300274\pi\)
−0.994611 + 0.103673i \(0.966940\pi\)
\(194\) 189.691 + 31.0468i 0.977791 + 0.160035i
\(195\) −8.20101 −0.0420565
\(196\) 0 0
\(197\) 124.117i 0.630034i 0.949086 + 0.315017i \(0.102010\pi\)
−0.949086 + 0.315017i \(0.897990\pi\)
\(198\) 23.5205 + 3.84961i 0.118791 + 0.0194425i
\(199\) 156.729 90.4874i 0.787581 0.454710i −0.0515289 0.998672i \(-0.516409\pi\)
0.839110 + 0.543961i \(0.183076\pi\)
\(200\) 6.67010 + 180.661i 0.0333505 + 0.903304i
\(201\) −56.9706 + 98.6759i −0.283436 + 0.490925i
\(202\) −36.6985 + 13.8707i −0.181676 + 0.0686669i
\(203\) 0 0
\(204\) −242.309 + 213.696i −1.18779 + 1.04753i
\(205\) −36.2000 20.9001i −0.176586 0.101952i
\(206\) 66.6851 + 54.5717i 0.323714 + 0.264911i
\(207\) −81.0488 + 46.7935i −0.391540 + 0.226056i
\(208\) 14.9859 19.7570i 0.0720477 0.0949856i
\(209\) −111.549 −0.533728
\(210\) 0 0
\(211\) 164.049 0.777482 0.388741 0.921347i \(-0.372910\pi\)
0.388741 + 0.921347i \(0.372910\pi\)
\(212\) −383.528 + 77.3998i −1.80909 + 0.365093i
\(213\) 302.180 174.464i 1.41869 0.819079i
\(214\) 19.7569 24.1423i 0.0923219 0.112815i
\(215\) 23.0478 + 13.3066i 0.107199 + 0.0618913i
\(216\) −153.137 81.0325i −0.708968 0.375151i
\(217\) 0 0
\(218\) 7.20606 2.72363i 0.0330553 0.0124937i
\(219\) −118.326 + 204.946i −0.540301 + 0.935829i
\(220\) 8.86455 26.3551i 0.0402934 0.119796i
\(221\) 31.7524 18.3322i 0.143676 0.0829513i
\(222\) −64.6127 + 394.774i −0.291048 + 1.77826i
\(223\) 10.5830i 0.0474574i 0.999718 + 0.0237287i \(0.00755379\pi\)
−0.999718 + 0.0237287i \(0.992446\pi\)
\(224\) 0 0
\(225\) 60.0395 0.266842
\(226\) 27.1875 + 4.44977i 0.120299 + 0.0196893i
\(227\) 52.9031 + 91.6308i 0.233053 + 0.403660i 0.958705 0.284402i \(-0.0917951\pi\)
−0.725652 + 0.688062i \(0.758462\pi\)
\(228\) −321.925 108.279i −1.41195 0.474910i
\(229\) −64.8469 37.4394i −0.283174 0.163491i 0.351685 0.936118i \(-0.385609\pi\)
−0.634860 + 0.772628i \(0.718942\pi\)
\(230\) 38.6030 + 102.134i 0.167839 + 0.444061i
\(231\) 0 0
\(232\) 84.0000 158.745i 0.362069 0.684246i
\(233\) 209.569 362.983i 0.899436 1.55787i 0.0712190 0.997461i \(-0.477311\pi\)
0.828217 0.560408i \(-0.189356\pi\)
\(234\) −6.37334 5.21563i −0.0272365 0.0222890i
\(235\) −28.0000 48.4974i −0.119149 0.206372i
\(236\) 48.7088 + 241.359i 0.206393 + 1.02271i
\(237\) 132.132i 0.557518i
\(238\) 0 0
\(239\) 148.318i 0.620577i 0.950642 + 0.310288i \(0.100426\pi\)
−0.950642 + 0.310288i \(0.899574\pi\)
\(240\) 51.1652 67.4546i 0.213188 0.281061i
\(241\) −229.936 398.261i −0.954092 1.65254i −0.736433 0.676510i \(-0.763492\pi\)
−0.217658 0.976025i \(-0.569842\pi\)
\(242\) −127.781 + 156.144i −0.528019 + 0.645224i
\(243\) −69.5894 + 120.532i −0.286376 + 0.496018i
\(244\) 99.6985 + 113.047i 0.408600 + 0.463309i
\(245\) 0 0
\(246\) −65.1127 172.272i −0.264686 0.700293i
\(247\) 33.3807 + 19.2724i 0.135145 + 0.0780258i
\(248\) 373.471 13.7888i 1.50593 0.0555998i
\(249\) −6.17157 10.6895i −0.0247854 0.0429296i
\(250\) 23.8306 145.602i 0.0953226 0.582407i
\(251\) −124.919 −0.497685 −0.248842 0.968544i \(-0.580050\pi\)
−0.248842 + 0.968544i \(0.580050\pi\)
\(252\) 0 0
\(253\) 157.993i 0.624478i
\(254\) −40.3882 + 246.766i −0.159009 + 0.971519i
\(255\) 108.409 62.5902i 0.425135 0.245452i
\(256\) 69.0091 + 246.523i 0.269567 + 0.962982i
\(257\) −213.676 + 370.098i −0.831425 + 1.44007i 0.0654835 + 0.997854i \(0.479141\pi\)
−0.896908 + 0.442216i \(0.854192\pi\)
\(258\) 41.4558 + 109.682i 0.160682 + 0.425123i
\(259\) 0 0
\(260\) −7.20606 + 6.35515i −0.0277156 + 0.0244429i
\(261\) −51.6552 29.8231i −0.197912 0.114265i
\(262\) −127.107 + 155.321i −0.485141 + 0.592828i
\(263\) 223.109 128.812i 0.848322 0.489779i −0.0117625 0.999931i \(-0.503744\pi\)
0.860084 + 0.510152i \(0.170411\pi\)
\(264\) 103.764 65.1276i 0.393046 0.246695i
\(265\) 151.598 0.572068
\(266\) 0 0
\(267\) 150.426 0.563395
\(268\) 26.4073 + 130.852i 0.0985348 + 0.488255i
\(269\) 186.408 107.623i 0.692968 0.400085i −0.111755 0.993736i \(-0.535647\pi\)
0.804723 + 0.593650i \(0.202314\pi\)
\(270\) 51.9511 + 42.5142i 0.192412 + 0.157460i
\(271\) 327.833 + 189.275i 1.20972 + 0.698431i 0.962698 0.270580i \(-0.0872154\pi\)
0.247020 + 0.969010i \(0.420549\pi\)
\(272\) −47.3137 + 375.541i −0.173947 + 1.38067i
\(273\) 0 0
\(274\) 40.5269 + 107.224i 0.147908 + 0.391329i
\(275\) 50.6791 87.7789i 0.184288 0.319196i
\(276\) −153.362 + 455.959i −0.555659 + 1.65202i
\(277\) −144.149 + 83.2243i −0.520393 + 0.300449i −0.737095 0.675789i \(-0.763803\pi\)
0.216703 + 0.976238i \(0.430470\pi\)
\(278\) −362.505 59.3312i −1.30397 0.213421i
\(279\) 124.117i 0.444863i
\(280\) 0 0
\(281\) −421.765 −1.50094 −0.750471 0.660904i \(-0.770173\pi\)
−0.750471 + 0.660904i \(0.770173\pi\)
\(282\) 39.8519 243.489i 0.141319 0.863437i
\(283\) −172.719 299.159i −0.610316 1.05710i −0.991187 0.132470i \(-0.957709\pi\)
0.380872 0.924628i \(-0.375624\pi\)
\(284\) 130.324 387.464i 0.458886 1.36431i
\(285\) 113.969 + 65.8000i 0.399891 + 0.230877i
\(286\) −13.0051 + 4.91545i −0.0454722 + 0.0171869i
\(287\) 0 0
\(288\) 82.6619 19.8821i 0.287021 0.0690350i
\(289\) −135.323 + 234.387i −0.468247 + 0.811028i
\(290\) −44.0711 + 53.8536i −0.151969 + 0.185702i
\(291\) −164.066 284.171i −0.563801 0.976532i
\(292\) 54.8471 + 271.776i 0.187833 + 0.930739i
\(293\) 511.038i 1.74416i −0.489365 0.872079i \(-0.662771\pi\)
0.489365 0.872079i \(-0.337229\pi\)
\(294\) 0 0
\(295\) 95.4028i 0.323399i
\(296\) 249.146 + 396.950i 0.841708 + 1.34105i
\(297\) 48.5685 + 84.1232i 0.163530 + 0.283243i
\(298\) −297.655 243.586i −0.998841 0.817402i
\(299\) 27.2965 47.2789i 0.0912925 0.158123i
\(300\) 231.463 204.131i 0.771543 0.680437i
\(301\) 0 0
\(302\) −214.683 + 81.1427i −0.710872 + 0.268684i
\(303\) 58.0010 + 33.4869i 0.191422 + 0.110518i
\(304\) −366.777 + 154.324i −1.20650 + 0.507644i
\(305\) −29.2010 50.5776i −0.0957410 0.165828i
\(306\) 124.055 + 20.3041i 0.405409 + 0.0663532i
\(307\) −223.331 −0.727462 −0.363731 0.931504i \(-0.618497\pi\)
−0.363731 + 0.931504i \(0.618497\pi\)
\(308\) 0 0
\(309\) 147.098i 0.476047i
\(310\) −142.903 23.3889i −0.460976 0.0754480i
\(311\) 10.7376 6.19938i 0.0345262 0.0199337i −0.482638 0.875820i \(-0.660321\pi\)
0.517164 + 0.855886i \(0.326988\pi\)
\(312\) −42.3032 + 1.56186i −0.135587 + 0.00500596i
\(313\) 205.024 355.113i 0.655030 1.13455i −0.326856 0.945074i \(-0.605989\pi\)
0.981886 0.189471i \(-0.0606774\pi\)
\(314\) 396.889 150.010i 1.26398 0.477739i
\(315\) 0 0
\(316\) 102.392 + 116.102i 0.324025 + 0.367410i
\(317\) 112.857 + 65.1580i 0.356016 + 0.205546i 0.667332 0.744761i \(-0.267436\pi\)
−0.311316 + 0.950306i \(0.600770\pi\)
\(318\) 516.900 + 423.006i 1.62547 + 1.33021i
\(319\) −87.2038 + 50.3472i −0.273366 + 0.157828i
\(320\) −7.31434 98.9200i −0.0228573 0.309125i
\(321\) −53.2548 −0.165903
\(322\) 0 0
\(323\) −588.347 −1.82151
\(324\) 77.4297 + 383.676i 0.238981 + 1.18419i
\(325\) −30.3311 + 17.5117i −0.0933266 + 0.0538821i
\(326\) −304.668 + 372.295i −0.934565 + 1.14201i
\(327\) −11.3890 6.57544i −0.0348287 0.0201084i
\(328\) −190.711 100.915i −0.581435 0.307666i
\(329\) 0 0
\(330\) −44.4020 + 16.7824i −0.134552 + 0.0508557i
\(331\) −107.130 + 185.555i −0.323655 + 0.560588i −0.981239 0.192794i \(-0.938245\pi\)
0.657584 + 0.753381i \(0.271579\pi\)
\(332\) −13.7064 4.61014i −0.0412842 0.0138859i
\(333\) 134.793 77.8227i 0.404783 0.233702i
\(334\) −68.5174 + 418.631i −0.205142 + 1.25339i
\(335\) 51.7223i 0.154395i
\(336\) 0 0
\(337\) 164.049 0.486792 0.243396 0.969927i \(-0.421739\pi\)
0.243396 + 0.969927i \(0.421739\pi\)
\(338\) −328.821 53.8181i −0.972843 0.159225i
\(339\) −23.5147 40.7287i −0.0693650 0.120144i
\(340\) 46.7545 139.006i 0.137513 0.408840i
\(341\) −181.461 104.766i −0.532143 0.307233i
\(342\) 46.7229 + 123.617i 0.136617 + 0.361454i
\(343\) 0 0
\(344\) 121.421 + 64.2501i 0.352969 + 0.186774i
\(345\) 93.1960 161.420i 0.270133 0.467884i
\(346\) −282.027 230.797i −0.815107 0.667043i
\(347\) 54.8457 + 94.9955i 0.158057 + 0.273762i 0.934168 0.356834i \(-0.116144\pi\)
−0.776111 + 0.630596i \(0.782810\pi\)
\(348\) −300.537 + 60.6513i −0.863611 + 0.174285i
\(349\) 463.479i 1.32802i −0.747723 0.664010i \(-0.768853\pi\)
0.747723 0.664010i \(-0.231147\pi\)
\(350\) 0 0
\(351\) 33.5648i 0.0956261i
\(352\) 40.7067 137.636i 0.115644 0.391010i
\(353\) 39.0488 + 67.6345i 0.110620 + 0.191599i 0.916020 0.401132i \(-0.131383\pi\)
−0.805401 + 0.592731i \(0.798050\pi\)
\(354\) 266.204 325.293i 0.751988 0.918907i
\(355\) −79.1960 + 137.171i −0.223087 + 0.386398i
\(356\) 132.177 116.569i 0.371283 0.327441i
\(357\) 0 0
\(358\) 40.4508 + 107.023i 0.112991 + 0.298946i
\(359\) 316.198 + 182.557i 0.880774 + 0.508515i 0.870913 0.491437i \(-0.163528\pi\)
0.00986020 + 0.999951i \(0.496861\pi\)
\(360\) −32.9193 + 1.21540i −0.0914424 + 0.00337611i
\(361\) −128.760 223.019i −0.356676 0.617780i
\(362\) 105.380 643.857i 0.291105 1.77861i
\(363\) 344.434 0.948853
\(364\) 0 0
\(365\) 107.426i 0.294316i
\(366\) 41.5613 253.933i 0.113555 0.693807i
\(367\) −191.165 + 110.369i −0.520887 + 0.300734i −0.737297 0.675568i \(-0.763898\pi\)
0.216411 + 0.976302i \(0.430565\pi\)
\(368\) 218.577 + 519.485i 0.593959 + 1.41164i
\(369\) −35.8284 + 62.0567i −0.0970960 + 0.168175i
\(370\) −64.2010 169.860i −0.173516 0.459081i
\(371\) 0 0
\(372\) −421.990 478.492i −1.13438 1.28627i
\(373\) −217.852 125.777i −0.584052 0.337203i 0.178690 0.983905i \(-0.442814\pi\)
−0.762742 + 0.646703i \(0.776147\pi\)
\(374\) 134.399 164.232i 0.359356 0.439123i
\(375\) −218.121 + 125.932i −0.581657 + 0.335820i
\(376\) −153.668 244.831i −0.408692 0.651147i
\(377\) 34.7939 0.0922916
\(378\) 0 0
\(379\) 286.024 0.754682 0.377341 0.926074i \(-0.376839\pi\)
0.377341 + 0.926074i \(0.376839\pi\)
\(380\) 151.132 30.5000i 0.397716 0.0802631i
\(381\) 369.672 213.430i 0.970268 0.560184i
\(382\) −150.233 122.943i −0.393279 0.321840i
\(383\) −92.5727 53.4468i −0.241704 0.139548i 0.374256 0.927326i \(-0.377898\pi\)
−0.615960 + 0.787778i \(0.711232\pi\)
\(384\) 251.078 357.695i 0.653850 0.931497i
\(385\) 0 0
\(386\) 111.230 + 294.288i 0.288162 + 0.762404i
\(387\) 22.8112 39.5101i 0.0589436 0.102093i
\(388\) −364.372 122.557i −0.939102 0.315867i
\(389\) 66.8405 38.5904i 0.171826 0.0992040i −0.411620 0.911355i \(-0.635037\pi\)
0.583447 + 0.812151i \(0.301704\pi\)
\(390\) 16.1866 + 2.64927i 0.0415042 + 0.00679300i
\(391\) 833.307i 2.13122i
\(392\) 0 0
\(393\) 342.617 0.871800
\(394\) 40.0949 244.974i 0.101764 0.621761i
\(395\) −29.9899 51.9440i −0.0759238 0.131504i
\(396\) −45.1798 15.1962i −0.114090 0.0383743i
\(397\) −569.424 328.757i −1.43432 0.828103i −0.436870 0.899525i \(-0.643913\pi\)
−0.997446 + 0.0714218i \(0.977246\pi\)
\(398\) −338.573 + 127.968i −0.850685 + 0.321529i
\(399\) 0 0
\(400\) 45.1960 358.732i 0.112990 0.896830i
\(401\) −159.397 + 276.084i −0.397499 + 0.688488i −0.993417 0.114557i \(-0.963455\pi\)
0.595918 + 0.803045i \(0.296788\pi\)
\(402\) 144.321 176.357i 0.359009 0.438698i
\(403\) 36.2010 + 62.7020i 0.0898288 + 0.155588i
\(404\) 76.9140 15.5220i 0.190381 0.0384209i
\(405\) 151.657i 0.374461i
\(406\) 0 0
\(407\) 262.759i 0.645600i
\(408\) 547.287 343.504i 1.34139 0.841923i
\(409\) 72.6325 + 125.803i 0.177585 + 0.307587i 0.941053 0.338259i \(-0.109838\pi\)
−0.763468 + 0.645846i \(0.776505\pi\)
\(410\) 64.6978 + 52.9455i 0.157799 + 0.129135i
\(411\) 97.8406 169.465i 0.238055 0.412323i
\(412\) −113.990 129.252i −0.276675 0.313719i
\(413\) 0 0
\(414\) 175.085 66.1760i 0.422911 0.159846i
\(415\) 4.85237 + 2.80152i 0.0116925 + 0.00675065i
\(416\) −35.9606 + 34.1541i −0.0864438 + 0.0821012i
\(417\) 313.534 + 543.057i 0.751880 + 1.30229i
\(418\) 220.169 + 36.0351i 0.526720 + 0.0862083i
\(419\) −707.012 −1.68738 −0.843690 0.536831i \(-0.819621\pi\)
−0.843690 + 0.536831i \(0.819621\pi\)
\(420\) 0 0
\(421\) 121.989i 0.289761i −0.989449 0.144880i \(-0.953720\pi\)
0.989449 0.144880i \(-0.0462798\pi\)
\(422\) −323.789 52.9946i −0.767273 0.125580i
\(423\) −83.1377 + 47.9996i −0.196543 + 0.113474i
\(424\) 781.987 28.8714i 1.84431 0.0680929i
\(425\) 267.299 462.975i 0.628938 1.08935i
\(426\) −652.784 + 246.729i −1.53236 + 0.579176i
\(427\) 0 0
\(428\) −46.7939 + 41.2684i −0.109332 + 0.0964214i
\(429\) 20.5541 + 11.8669i 0.0479118 + 0.0276619i
\(430\) −41.1917 33.7092i −0.0957946 0.0783936i
\(431\) 509.969 294.431i 1.18322 0.683133i 0.226464 0.974020i \(-0.427283\pi\)
0.956758 + 0.290886i \(0.0939501\pi\)
\(432\) 276.076 + 209.407i 0.639064 + 0.484738i
\(433\) −137.696 −0.318004 −0.159002 0.987278i \(-0.550828\pi\)
−0.159002 + 0.987278i \(0.550828\pi\)
\(434\) 0 0
\(435\) 118.794 0.273090
\(436\) −15.1027 + 3.04788i −0.0346393 + 0.00699056i
\(437\) −758.675 + 438.021i −1.73610 + 1.00234i
\(438\) 299.751 366.287i 0.684362 0.836271i
\(439\) 381.522 + 220.272i 0.869070 + 0.501758i 0.867039 0.498240i \(-0.166020\pi\)
0.00203069 + 0.999998i \(0.499354\pi\)
\(440\) −26.0101 + 49.1545i −0.0591139 + 0.111715i
\(441\) 0 0
\(442\) −68.5929 + 25.9257i −0.155188 + 0.0586554i
\(443\) 243.529 421.805i 0.549727 0.952155i −0.448566 0.893750i \(-0.648065\pi\)
0.998293 0.0584052i \(-0.0186015\pi\)
\(444\) 255.057 758.309i 0.574453 1.70790i
\(445\) −59.1361 + 34.1422i −0.132890 + 0.0767241i
\(446\) 3.41875 20.8881i 0.00766537 0.0468343i
\(447\) 656.587i 1.46887i
\(448\) 0 0
\(449\) 264.039 0.588059 0.294030 0.955796i \(-0.405004\pi\)
0.294030 + 0.955796i \(0.405004\pi\)
\(450\) −118.502 19.3953i −0.263339 0.0431006i
\(451\) 60.4853 + 104.764i 0.134114 + 0.232292i
\(452\) −52.2235 17.5654i −0.115539 0.0388615i
\(453\) 339.301 + 195.896i 0.749010 + 0.432441i
\(454\) −74.8162 197.945i −0.164793 0.436003i
\(455\) 0 0
\(456\) 600.416 + 317.710i 1.31670 + 0.696733i
\(457\) 257.161 445.417i 0.562717 0.974654i −0.434542 0.900652i \(-0.643090\pi\)
0.997258 0.0740019i \(-0.0235771\pi\)
\(458\) 115.896 + 94.8438i 0.253049 + 0.207083i
\(459\) 256.167 + 443.693i 0.558097 + 0.966652i
\(460\) −43.1987 214.056i −0.0939103 0.465340i
\(461\) 202.224i 0.438664i −0.975650 0.219332i \(-0.929612\pi\)
0.975650 0.219332i \(-0.0703878\pi\)
\(462\) 0 0
\(463\) 722.653i 1.56081i 0.625277 + 0.780403i \(0.284986\pi\)
−0.625277 + 0.780403i \(0.715014\pi\)
\(464\) −217.075 + 286.186i −0.467835 + 0.616780i
\(465\) 123.598 + 214.078i 0.265802 + 0.460383i
\(466\) −530.892 + 648.735i −1.13925 + 1.39213i
\(467\) −173.641 + 300.755i −0.371822 + 0.644015i −0.989846 0.142144i \(-0.954600\pi\)
0.618023 + 0.786160i \(0.287934\pi\)
\(468\) 10.8944 + 12.3531i 0.0232787 + 0.0263956i
\(469\) 0 0
\(470\) 39.5980 + 104.766i 0.0842510 + 0.222907i
\(471\) −627.273 362.156i −1.33179 0.768910i
\(472\) −18.1692 492.115i −0.0384940 1.04262i
\(473\) −38.5097 66.7007i −0.0814158 0.141016i
\(474\) 42.6841 260.794i 0.0900509 0.550198i
\(475\) 562.013 1.18319
\(476\) 0 0
\(477\) 259.880i 0.544822i
\(478\) 47.9129 292.741i 0.100236 0.612428i
\(479\) 25.2716 14.5906i 0.0527591 0.0304605i −0.473388 0.880854i \(-0.656969\pi\)
0.526148 + 0.850393i \(0.323636\pi\)
\(480\) −122.777 + 116.609i −0.255786 + 0.242936i
\(481\) −45.3970 + 78.6299i −0.0943804 + 0.163472i
\(482\) 325.179 + 860.342i 0.674645 + 1.78494i
\(483\) 0 0
\(484\) 302.647 266.909i 0.625303 0.551466i
\(485\) 128.996 + 74.4760i 0.265972 + 0.153559i
\(486\) 176.288 215.419i 0.362733 0.443249i
\(487\) −607.640 + 350.821i −1.24772 + 0.720372i −0.970654 0.240478i \(-0.922696\pi\)
−0.277067 + 0.960851i \(0.589362\pi\)
\(488\) −160.260 255.333i −0.328401 0.523223i
\(489\) 821.235 1.67942
\(490\) 0 0
\(491\) −59.9512 −0.122100 −0.0610501 0.998135i \(-0.519445\pi\)
−0.0610501 + 0.998135i \(0.519445\pi\)
\(492\) 72.8644 + 361.054i 0.148098 + 0.733850i
\(493\) −459.942 + 265.548i −0.932945 + 0.538636i
\(494\) −59.6590 48.8220i −0.120767 0.0988299i
\(495\) 15.9947 + 9.23455i 0.0323125 + 0.0186557i
\(496\) −741.588 93.4313i −1.49514 0.188370i
\(497\) 0 0
\(498\) 8.72792 + 23.0919i 0.0175259 + 0.0463693i
\(499\) 42.1421 72.9923i 0.0844532 0.146277i −0.820705 0.571352i \(-0.806419\pi\)
0.905158 + 0.425075i \(0.139752\pi\)
\(500\) −94.0709 + 279.681i −0.188142 + 0.559363i
\(501\) 627.138 362.079i 1.25177 0.722712i
\(502\) 246.557 + 40.3540i 0.491150 + 0.0803865i
\(503\) 409.987i 0.815083i 0.913187 + 0.407542i \(0.133614\pi\)
−0.913187 + 0.407542i \(0.866386\pi\)
\(504\) 0 0
\(505\) −30.4020 −0.0602020
\(506\) 51.0384 311.837i 0.100866 0.616278i
\(507\) 284.401 + 492.596i 0.560948 + 0.971590i
\(508\) 159.431 474.004i 0.313841 0.933079i
\(509\) −413.123 238.516i −0.811636 0.468598i 0.0358878 0.999356i \(-0.488574\pi\)
−0.847524 + 0.530758i \(0.821907\pi\)
\(510\) −234.191 + 88.5158i −0.459198 + 0.173560i
\(511\) 0 0
\(512\) −56.5685 508.865i −0.110485 0.993878i
\(513\) −269.304 + 466.448i −0.524958 + 0.909254i
\(514\) 541.298 661.450i 1.05311 1.28687i
\(515\) 33.3869 + 57.8278i 0.0648289 + 0.112287i
\(516\) −46.3912 229.875i −0.0899054 0.445495i
\(517\) 162.065i 0.313472i
\(518\) 0 0
\(519\) 622.114i 1.19868i
\(520\) 16.2759 10.2155i 0.0312997 0.0196453i
\(521\) 105.437 + 182.621i 0.202373 + 0.350521i 0.949293 0.314394i \(-0.101801\pi\)
−0.746919 + 0.664915i \(0.768468\pi\)
\(522\) 92.3196 + 75.5498i 0.176858 + 0.144731i
\(523\) 255.783 443.030i 0.489069 0.847093i −0.510852 0.859669i \(-0.670670\pi\)
0.999921 + 0.0125761i \(0.00400319\pi\)
\(524\) 301.051 265.502i 0.574525 0.506683i
\(525\) 0 0
\(526\) −481.970 + 182.167i −0.916292 + 0.346326i
\(527\) −957.084 552.573i −1.81610 1.04852i
\(528\) −225.842 + 95.0247i −0.427732 + 0.179971i
\(529\) 355.892 + 616.423i 0.672764 + 1.16526i
\(530\) −299.215 48.9725i −0.564556 0.0924009i
\(531\) −163.546 −0.307997
\(532\) 0 0
\(533\) 41.8002i 0.0784244i
\(534\) −296.902 48.5940i −0.555997 0.0910001i
\(535\) 20.9357 12.0872i 0.0391321 0.0225929i
\(536\) −9.85037 266.799i −0.0183776 0.497759i
\(537\) 97.6569 169.147i 0.181856 0.314984i
\(538\) −402.688 + 152.202i −0.748491 + 0.282903i
\(539\) 0 0
\(540\) −88.8040 100.694i −0.164452 0.186471i
\(541\) 296.542 + 171.208i 0.548136 + 0.316466i 0.748370 0.663282i \(-0.230837\pi\)
−0.200234 + 0.979748i \(0.564170\pi\)
\(542\) −585.914 479.483i −1.08102 0.884654i
\(543\) −964.542 + 556.878i −1.77632 + 1.02556i
\(544\) 214.700 725.935i 0.394670 1.33444i
\(545\) 5.96970 0.0109536
\(546\) 0 0
\(547\) −441.976 −0.807999 −0.404000 0.914759i \(-0.632380\pi\)
−0.404000 + 0.914759i \(0.632380\pi\)
\(548\) −45.3516 224.724i −0.0827585 0.410081i
\(549\) −86.7038 + 50.0584i −0.157930 + 0.0911811i
\(550\) −128.384 + 156.881i −0.233425 + 0.285238i
\(551\) −483.529 279.166i −0.877548 0.506653i
\(552\) 449.990 850.401i 0.815199 1.54058i
\(553\) 0 0
\(554\) 311.397 117.697i 0.562088 0.212449i
\(555\) −154.995 + 268.459i −0.279270 + 0.483710i
\(556\) 696.323 + 234.208i 1.25238 + 0.421238i
\(557\) −316.714 + 182.855i −0.568607 + 0.328285i −0.756593 0.653886i \(-0.773137\pi\)
0.187986 + 0.982172i \(0.439804\pi\)
\(558\) −40.0949 + 244.974i −0.0718546 + 0.439021i
\(559\) 26.6133i 0.0476087i
\(560\) 0 0
\(561\) −362.274 −0.645765
\(562\) 832.453 + 136.248i 1.48123 + 0.242433i
\(563\) 403.194 + 698.353i 0.716154 + 1.24041i 0.962513 + 0.271236i \(0.0874323\pi\)
−0.246359 + 0.969179i \(0.579234\pi\)
\(564\) −157.315 + 467.711i −0.278926 + 0.829274i
\(565\) 18.4883 + 10.6743i 0.0327227 + 0.0188925i
\(566\) 244.262 + 646.256i 0.431558 + 1.14180i
\(567\) 0 0
\(568\) −382.392 + 722.653i −0.673225 + 1.27228i
\(569\) −111.446 + 193.030i −0.195862 + 0.339244i −0.947183 0.320694i \(-0.896084\pi\)
0.751320 + 0.659938i \(0.229417\pi\)
\(570\) −203.689 166.689i −0.357349 0.292436i
\(571\) −286.541 496.304i −0.501823 0.869184i −0.999998 0.00210683i \(-0.999329\pi\)
0.498174 0.867077i \(-0.334004\pi\)
\(572\) 27.2565 5.50063i 0.0476512 0.00961649i
\(573\) 331.393i 0.578348i
\(574\) 0 0
\(575\) 796.008i 1.38436i
\(576\) −169.576 + 12.5388i −0.294402 + 0.0217687i
\(577\) −361.950 626.916i −0.627297 1.08651i −0.988092 0.153865i \(-0.950828\pi\)
0.360795 0.932645i \(-0.382505\pi\)
\(578\) 342.810 418.903i 0.593097 0.724746i
\(579\) 268.534 465.115i 0.463789 0.803307i
\(580\) 104.382 92.0561i 0.179969 0.158717i
\(581\) 0 0
\(582\) 232.024 + 613.879i 0.398667 + 1.05477i
\(583\) −379.949 219.364i −0.651714 0.376267i
\(584\) −20.4589 554.132i −0.0350323 0.948856i
\(585\) −3.19091 5.52682i −0.00545455 0.00944755i
\(586\) −165.087 + 1008.66i −0.281718 + 1.72126i
\(587\) −21.1198 −0.0359793 −0.0179896 0.999838i \(-0.505727\pi\)
−0.0179896 + 0.999838i \(0.505727\pi\)
\(588\) 0 0
\(589\) 1161.82i 1.97253i
\(590\) −30.8191 + 188.300i −0.0522358 + 0.319153i
\(591\) −366.988 + 211.880i −0.620960 + 0.358512i
\(592\) −363.517 863.960i −0.614049 1.45939i
\(593\) −64.3726 + 111.497i −0.108554 + 0.188021i −0.915185 0.403035i \(-0.867955\pi\)
0.806631 + 0.591056i \(0.201289\pi\)
\(594\) −68.6863 181.727i −0.115633 0.305937i
\(595\) 0 0
\(596\) 508.804 + 576.930i 0.853698 + 0.968003i
\(597\) 535.105 + 308.943i 0.896324 + 0.517493i
\(598\) −69.1491 + 84.4982i −0.115634 + 0.141301i
\(599\) 280.705 162.065i 0.468623 0.270559i −0.247040 0.969005i \(-0.579458\pi\)
0.715663 + 0.698446i \(0.246125\pi\)
\(600\) −522.790 + 328.129i −0.871317 + 0.546882i
\(601\) 721.862 1.20110 0.600551 0.799587i \(-0.294948\pi\)
0.600551 + 0.799587i \(0.294948\pi\)
\(602\) 0 0
\(603\) −88.6661 −0.147042
\(604\) 449.941 90.8027i 0.744936 0.150336i
\(605\) −135.405 + 78.1759i −0.223809 + 0.129216i
\(606\) −103.661 84.8311i −0.171058 0.139985i
\(607\) 611.413 + 353.000i 1.00727 + 0.581548i 0.910391 0.413748i \(-0.135781\pi\)
0.0968795 + 0.995296i \(0.469114\pi\)
\(608\) 773.775 186.110i 1.27266 0.306103i
\(609\) 0 0
\(610\) 41.2965 + 109.260i 0.0676991 + 0.179115i
\(611\) 28.0000 48.4974i 0.0458265 0.0793739i
\(612\) −238.293 80.1499i −0.389368 0.130964i
\(613\) 18.9026 10.9134i 0.0308363 0.0178033i −0.484503 0.874790i \(-0.660999\pi\)
0.515339 + 0.856986i \(0.327666\pi\)
\(614\) 440.797 + 72.1453i 0.717910 + 0.117500i
\(615\) 142.715i 0.232057i
\(616\) 0 0
\(617\) −699.578 −1.13384 −0.566919 0.823774i \(-0.691865\pi\)
−0.566919 + 0.823774i \(0.691865\pi\)
\(618\) −47.5190 + 290.334i −0.0768915 + 0.469796i
\(619\) 48.0990 + 83.3100i 0.0777044 + 0.134588i 0.902259 0.431194i \(-0.141908\pi\)
−0.824555 + 0.565782i \(0.808574\pi\)
\(620\) 274.497 + 92.3271i 0.442737 + 0.148915i
\(621\) 660.654 + 381.429i 1.06386 + 0.614217i
\(622\) −23.1960 + 8.76725i −0.0372925 + 0.0140953i
\(623\) 0 0
\(624\) 84.0000 + 10.5830i 0.134615 + 0.0169599i
\(625\) −225.309 + 390.247i −0.360495 + 0.624395i
\(626\) −519.381 + 634.668i −0.829682 + 1.01385i
\(627\) −190.426 329.828i −0.303710 0.526042i
\(628\) −831.815 + 167.869i −1.32455 + 0.267307i
\(629\) 1385.88i 2.20331i
\(630\) 0 0
\(631\) 269.399i 0.426940i 0.976950 + 0.213470i \(0.0684766\pi\)
−0.976950 + 0.213470i \(0.931523\pi\)
\(632\) −164.589 262.231i −0.260426 0.414922i
\(633\) 280.049 + 485.059i 0.442415 + 0.766285i
\(634\) −201.701 165.062i −0.318141 0.260351i
\(635\) −96.8843 + 167.809i −0.152574 + 0.264266i
\(636\) −883.578 1001.88i −1.38927 1.57529i
\(637\) 0 0
\(638\) 188.382 71.2016i 0.295269 0.111601i
\(639\) 235.149 + 135.763i 0.367995 + 0.212462i
\(640\) −17.5187 + 197.605i −0.0273730 + 0.308758i
\(641\) −317.907 550.630i −0.495954 0.859018i 0.504035 0.863683i \(-0.331848\pi\)
−0.999989 + 0.00466541i \(0.998515\pi\)
\(642\) 105.111 + 17.2035i 0.163724 + 0.0267968i
\(643\) −1281.70 −1.99332 −0.996658 0.0816828i \(-0.973971\pi\)
−0.996658 + 0.0816828i \(0.973971\pi\)
\(644\) 0 0
\(645\) 90.8634i 0.140874i
\(646\) 1161.24 + 190.061i 1.79759 + 0.294212i
\(647\) 225.826 130.381i 0.349035 0.201516i −0.315225 0.949017i \(-0.602080\pi\)
0.664260 + 0.747501i \(0.268747\pi\)
\(648\) −28.8826 782.290i −0.0445719 1.20724i
\(649\) −138.049 + 239.107i −0.212710 + 0.368424i
\(650\) 65.5227 24.7653i 0.100804 0.0381004i
\(651\) 0 0
\(652\) 721.602 636.393i 1.10675 0.976063i
\(653\) 944.471 + 545.291i 1.44636 + 0.835055i 0.998262 0.0589313i \(-0.0187693\pi\)
0.448095 + 0.893986i \(0.352103\pi\)
\(654\) 20.3547 + 16.6573i 0.0311235 + 0.0254699i
\(655\) −134.691 + 77.7637i −0.205635 + 0.118723i
\(656\) 343.813 + 260.787i 0.524106 + 0.397541i
\(657\) −184.156 −0.280299
\(658\) 0 0
\(659\) −362.780 −0.550500 −0.275250 0.961373i \(-0.588761\pi\)
−0.275250 + 0.961373i \(0.588761\pi\)
\(660\) 93.0594 18.7803i 0.140999 0.0284550i
\(661\) −102.047 + 58.9169i −0.154383 + 0.0891330i −0.575201 0.818012i \(-0.695076\pi\)
0.420818 + 0.907145i \(0.361743\pi\)
\(662\) 271.388 331.629i 0.409952 0.500950i
\(663\) 108.409 + 62.5902i 0.163513 + 0.0944045i
\(664\) 25.5635 + 13.5269i 0.0384992 + 0.0203719i
\(665\) 0 0
\(666\) −291.186 + 110.058i −0.437216 + 0.165252i
\(667\) −395.397 + 684.848i −0.592799 + 1.02676i
\(668\) 270.471 804.135i 0.404897 1.20379i
\(669\) −31.2918 + 18.0663i −0.0467740 + 0.0270050i
\(670\) −16.7085 + 102.086i −0.0249380 + 0.152368i
\(671\) 169.017i 0.251888i
\(672\) 0 0
\(673\) −6.56854 −0.00976009 −0.00488005 0.999988i \(-0.501553\pi\)
−0.00488005 + 0.999988i \(0.501553\pi\)
\(674\) −323.789 52.9946i −0.480400 0.0786270i
\(675\) −244.701 423.834i −0.362519 0.627902i
\(676\) 631.621 + 212.446i 0.934350 + 0.314269i
\(677\) 108.942 + 62.8978i 0.160919 + 0.0929066i 0.578297 0.815826i \(-0.303718\pi\)
−0.417378 + 0.908733i \(0.637051\pi\)
\(678\) 33.2548 + 87.9840i 0.0490484 + 0.129770i
\(679\) 0 0
\(680\) −137.186 + 259.257i −0.201744 + 0.381260i
\(681\) −180.622 + 312.847i −0.265231 + 0.459394i
\(682\) 324.312 + 265.401i 0.475531 + 0.389151i
\(683\) 276.887 + 479.583i 0.405399 + 0.702171i 0.994368 0.105984i \(-0.0337994\pi\)
−0.588969 + 0.808156i \(0.700466\pi\)
\(684\) −52.2852 259.081i −0.0764404 0.378774i
\(685\) 88.8274i 0.129675i
\(686\) 0 0
\(687\) 255.652i 0.372128i
\(688\) −218.899 166.037i −0.318166 0.241333i
\(689\) 75.7990 + 131.288i 0.110013 + 0.190548i
\(690\) −236.090 + 288.495i −0.342159 + 0.418109i
\(691\) −523.413 + 906.577i −0.757471 + 1.31198i 0.186665 + 0.982424i \(0.440232\pi\)
−0.944136 + 0.329555i \(0.893101\pi\)
\(692\) 482.090 + 546.639i 0.696662 + 0.789941i
\(693\) 0 0
\(694\) −77.5635 205.214i −0.111763 0.295697i
\(695\) −246.515 142.325i −0.354698 0.204785i
\(696\) 612.774 22.6240i 0.880422 0.0325057i
\(697\) 319.019 + 552.558i 0.457703 + 0.792766i
\(698\) −149.723 + 914.787i −0.214503 + 1.31058i
\(699\) 1431.02 2.04724
\(700\) 0 0
\(701\) 625.993i 0.893000i −0.894784 0.446500i \(-0.852670\pi\)
0.894784 0.446500i \(-0.147330\pi\)
\(702\) −10.8428 + 66.2481i −0.0154456 + 0.0943705i
\(703\) 1261.76 728.476i 1.79482 1.03624i
\(704\) −124.806 + 258.507i −0.177282 + 0.367197i
\(705\) 95.5980 165.581i 0.135600 0.234866i
\(706\) −55.2233 146.107i −0.0782200 0.206951i
\(707\) 0 0
\(708\) −630.500 + 556.048i −0.890536 + 0.785379i
\(709\) −513.979 296.746i −0.724935 0.418541i 0.0916314 0.995793i \(-0.470792\pi\)
−0.816566 + 0.577252i \(0.804125\pi\)
\(710\) 200.624 245.157i 0.282569 0.345291i
\(711\) −89.0461 + 51.4108i −0.125241 + 0.0723077i
\(712\) −298.539 + 187.378i −0.419296 + 0.263171i
\(713\) −1645.55 −2.30792
\(714\) 0 0
\(715\) −10.7737 −0.0150682
\(716\) −45.2665 224.302i −0.0632213 0.313271i
\(717\) −438.546 + 253.194i −0.611640 + 0.353130i
\(718\) −565.118 462.465i −0.787073 0.644101i
\(719\) −529.578 305.752i −0.736549 0.425247i 0.0842645 0.996443i \(-0.473146\pi\)
−0.820813 + 0.571197i \(0.806479\pi\)
\(720\) 65.3667 + 8.23543i 0.0907870 + 0.0114381i
\(721\) 0 0
\(722\) 182.094 + 481.775i 0.252208 + 0.667279i
\(723\) 785.051 1359.75i 1.08582 1.88070i
\(724\) −415.985 + 1236.76i −0.574566 + 1.70824i
\(725\) 439.355 253.662i 0.606007 0.349878i
\(726\) −679.822 111.266i −0.936394 0.153260i
\(727\) 944.144i 1.29868i −0.760496 0.649342i \(-0.775044\pi\)
0.760496 0.649342i \(-0.224956\pi\)
\(728\) 0 0
\(729\) 405.489 0.556227
\(730\) −34.7029 + 212.030i −0.0475383 + 0.290452i
\(731\) −203.113 351.802i −0.277856 0.481261i
\(732\) −164.062 + 487.772i −0.224129 + 0.666355i
\(733\) −189.014 109.127i −0.257863 0.148878i 0.365496 0.930813i \(-0.380899\pi\)
−0.623360 + 0.781935i \(0.714233\pi\)
\(734\) 412.965 156.086i 0.562622 0.212651i
\(735\) 0 0
\(736\) −263.598 1095.94i −0.358149 1.48905i
\(737\) −74.8427 + 129.631i −0.101550 + 0.175891i
\(738\) 90.7628 110.910i 0.122985 0.150284i
\(739\) 3.64971 + 6.32149i 0.00493872 + 0.00855411i 0.868484 0.495717i \(-0.165095\pi\)
−0.863545 + 0.504271i \(0.831761\pi\)
\(740\) 71.8441 + 355.999i 0.0970867 + 0.481079i
\(741\) 131.600i 0.177598i
\(742\) 0 0
\(743\) 106.867i 0.143832i −0.997411 0.0719159i \(-0.977089\pi\)
0.997411 0.0719159i \(-0.0229113\pi\)
\(744\) 678.325 + 1080.74i 0.911727 + 1.45260i
\(745\) −149.025 258.119i −0.200034 0.346469i
\(746\) 389.351 + 318.625i 0.521918 + 0.427112i
\(747\) 4.80256 8.31828i 0.00642913 0.0111356i
\(748\) −318.323 + 280.734i −0.425565 + 0.375313i
\(749\) 0 0
\(750\) 471.196 178.095i 0.628261 0.237460i
\(751\) −110.387 63.7317i −0.146986 0.0848624i 0.424703 0.905333i \(-0.360378\pi\)
−0.571689 + 0.820470i \(0.693712\pi\)
\(752\) 224.210 + 532.874i 0.298152 + 0.708609i
\(753\) −213.250 369.359i −0.283200 0.490517i
\(754\) −68.6741 11.2399i −0.0910798 0.0149070i
\(755\) −177.849 −0.235562
\(756\) 0 0
\(757\) 704.275i 0.930350i 0.885219 + 0.465175i \(0.154009\pi\)
−0.885219 + 0.465175i \(0.845991\pi\)
\(758\) −564.537 92.3979i −0.744772 0.121897i
\(759\) −467.153 + 269.711i −0.615485 + 0.355350i
\(760\) −308.148 + 11.3770i −0.405458 + 0.0149697i
\(761\) −501.465 + 868.563i −0.658955 + 1.14134i 0.321931 + 0.946763i \(0.395668\pi\)
−0.980886 + 0.194581i \(0.937665\pi\)
\(762\) −798.583 + 301.836i −1.04801 + 0.396110i
\(763\) 0 0
\(764\) 256.804 + 291.188i 0.336131 + 0.381137i
\(765\) 84.3614 + 48.7061i 0.110276 + 0.0636681i
\(766\) 165.449 + 135.395i 0.215990 + 0.176756i
\(767\) 82.6213 47.7014i 0.107720 0.0621922i
\(768\) −611.113 + 624.887i −0.795720 + 0.813655i
\(769\) 646.950 0.841288 0.420644 0.907226i \(-0.361804\pi\)
0.420644 + 0.907226i \(0.361804\pi\)
\(770\) 0 0
\(771\) −1459.07 −1.89244
\(772\) −124.472 616.780i −0.161234 0.798938i
\(773\) 488.668 282.132i 0.632170 0.364984i −0.149422 0.988774i \(-0.547741\pi\)
0.781592 + 0.623790i \(0.214408\pi\)
\(774\) −57.7867 + 70.6137i −0.0746599 + 0.0912322i
\(775\) 914.245 + 527.840i 1.17967 + 0.681083i
\(776\) 679.584 + 359.602i 0.875752 + 0.463404i
\(777\) 0 0
\(778\) −144.392 + 54.5750i −0.185594 + 0.0701478i
\(779\) −335.380 + 580.895i −0.430526 + 0.745693i
\(780\) −31.0924 10.4579i −0.0398620